This preview shows pages 1–4. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: garcia (jjg2564) HW 10 gualdani (56410) 1 This printout should have 23 questions. Multiplechoice questions may continue on the next column or page find all choices before answering. 001 10.0 points Let f be the function defined by f ( x ) = 3 + 2 x 1 / 3 . Consider the following properties: A. derivative exists for all x negationslash = 0 ; B. concave up on (0 , ) ; C. has horizontal tangent at x = 0 . Which does f have? 1. B only 2. A only correct 3. None of them 4. B and C only 5. A and B only 6. A and C only 7. C only 8. All of them Explanation: The graph of f is 2 4 2 4 2 4 6 On the other hand, after differentiation, f ( x ) = 2 3 x 2 / 3 , f ( x ) = 4 9 x 5 / 3 . Consequently, A. has: ( f ( x ) = (2 / 3) x 2 / 3 , x negationslash = 0); B. not have: ( f ( x ) < , x > 0); C. not have: (see graph). 002 10.0 points If f is increasing and its graph is concave down on (0 , 1), which of the following could be the graph of the derivative , f , of f ? 1. 1 f ( x ) 2. f ( x ) 1 3. 1 f ( x ) garcia (jjg2564) HW 10 gualdani (56410) 2 4. f ( x ) 1 cor rect Explanation: The function f increases when f > 0 on (0 , 1), and its graph is concave down when f < 0. Thus on (0 , 1) the graph of f lies above the xaxis and is decreasing. Of the four graphs, only f ( x ) 1 has these properties. 003 10.0 points When Sue uses first and second derivatives to analyze a particular continuous function y = f ( x ) she obtains the chart y y y x < 3 + x = 3 4 3 < x < x = 0 1 1 < x < 2 + x = 2 1 DNE x > 2 + + Which of the following can she conclude from her chart? A. f has a point of inflection at x = 2. B. f is concave down on ( , 0) . C. f is concave up on (0 , 2) . 1. none of them 2. A only 3. all of them 4. C only 5. B only 6. B and C only correct 7. A and C only 8. A and B only Explanation: The graph of f must look like 2 2 4 2 4 Consequently, A. False. B. True. C. True. 004 10.0 points The figure below shows the graphs of three functions: garcia (jjg2564) HW 10 gualdani (56410) 3 One is the graph of a function f , one is its derivative f , and one is its second derivative f . Identify which graph goes with which function. 1. f : f : f : 2. f : f : f : 3. f : f : f : 4. f : f : f : 5. f : f : f : correct 6. f : f : f : Explanation: Calculus tells us that f (i) has horizontal tangent at ( x , f ( x )) when f crosses the xaxis, (ii) is increasing when f > 0, and (iii) is decreasing when f < 0, (iv) has a local max at x when f ( x ) = 0 and f ( x ) < 0, (v) has a local min at x when f ( x ) = 0 and f ( x ) > 0, (vi) is concave up when f > 0, (v) and concave down when f < 0....
View Full
Document
 Fall '09
 Gualdani

Click to edit the document details